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Question

lf f(x)=x22, if 0x1,f(x)=2x23x+32 , lf 1x2 then the function f′′ is

A
Continuous
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B
Discontinuous
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C
Differentiable
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D
Not differentiable
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Solution

The correct options are
A Not differentiable
C Discontinuous
f(x)=⎪ ⎪⎪ ⎪x22,0x12x23x+32,1x2

f(x)={2x,0x14x3,1x2

f′′(x)={2,0x14,1x2

Clearly f′′(1)=2f(1+)=4 f'' is discontinuous
Hence it is also non differentiable

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